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Table
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Table

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Table[expr,n]

generates a list of n copies of expr.

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Table[expr,{i,imax}]

generates a list of the values of expr when i runs from 1 to imax.

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Table[expr,{i,imin,imax}]

starts with i=imin.

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Table[expr,{i,imin,imax,di}]

uses steps di.

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Table[expr,{i,{i1,i2,…}}]

uses the successive values i1, i2, ….

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Table[expr,{i,imin,imax},{j,jmin,jmax},…]

gives a nested list. The list associated with i is outermost. »

Details

  • You can use Table to build up vectors, matrices, tensors, and other arrays.
  • Table uses the standard Wolfram Language iteration specification.
  • Table evaluates its arguments in a nonstandard way.
  • Table[expr,spec] first evaluates spec, then localizes the variable specified and successively assigns values to it, each time evaluating expr.
  • Table effectively uses Block to localize values or variables.
  • Table[expr,spec1,spec2] is effectively equivalent to Table[Table[expr,spec2],spec1].
  • Parallelize[Table[expr,iter]] or ParallelTable[expr,iter] computes Table[expr,iter] in parallel on all subkernels. »

Examples

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Basic Examples  (6)Summary of the most common use cases

A table of the first 10 squares:

In[1]:=1
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https://wolfram.com/xid/0gisaa-j9w
Out[1]=1

A table with running from 0 to 20 in steps of 2:

In[1]:=1
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https://wolfram.com/xid/0gisaa-bd0
Out[1]=1

A list of 10 's:

In[1]:=1
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https://wolfram.com/xid/0gisaa-dm0
Out[1]=1

Make a 4×3 matrix:

In[1]:=1
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https://wolfram.com/xid/0gisaa-uth
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0gisaa-nux

Plot a table:

In[1]:=1
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https://wolfram.com/xid/0gisaa-nd9
Out[1]=1

Arrange a table in a column:

In[1]:=1
✖
https://wolfram.com/xid/0gisaa-nor
Out[1]=1

Scope  (6)Survey of the scope of standard use cases

The index in the table can run backward:

In[1]:=1
✖
https://wolfram.com/xid/0gisaa-b2n
Out[1]=1

Make a triangular array:

In[1]:=1
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https://wolfram.com/xid/0gisaa-eu6
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0gisaa-fpi

Make a 3×2×4 array, or tensor:

In[1]:=1
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https://wolfram.com/xid/0gisaa-n5r
Out[1]=1

Iterate over an existing list:

In[1]:=1
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https://wolfram.com/xid/0gisaa-ragly9
Out[1]=1

Make an array from existing lists:

In[1]:=1
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https://wolfram.com/xid/0gisaa-cdobrh
Out[1]=1

Table evaluates the expression separately each time:

In[1]:=1
✖
https://wolfram.com/xid/0gisaa-ui1ns7
Out[1]=1

Generalizations & Extensions  (3)Generalized and extended use cases

The table index can have symbolic values:

In[1]:=1
✖
https://wolfram.com/xid/0gisaa-bql
Out[1]=1

The variables need not just be symbols:

In[1]:=1
✖
https://wolfram.com/xid/0gisaa-ebk
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0gisaa-wez
Out[2]=2

ParallelTable computes Table in parallel:

In[1]:=1
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https://wolfram.com/xid/0gisaa-oejvh4
Out[1]=1

Table can be parallelized automatically, effectively using ParallelTable:

In[2]:=2
✖
https://wolfram.com/xid/0gisaa-q0irvc
Out[2]=2

Applications  (4)Sample problems that can be solved with this function

Make a table of graphics:

In[1]:=1
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https://wolfram.com/xid/0gisaa-kf5
Out[1]=1

Generate the corners of a polygon:

In[1]:=1
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https://wolfram.com/xid/0gisaa-e3k
Out[1]=1

Make Pascal's triangle:

In[1]:=1
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https://wolfram.com/xid/0gisaa-bdb
Out[1]=1

Compare font sizes from 10 points to 20 points:

In[1]:=1
✖
https://wolfram.com/xid/0gisaa-p5y
Out[1]=1

Properties & Relations  (13)Properties of the function, and connections to other functions

Display of Tables  (5)

Use ListPlot, ListLinePlot and similar functions to visualize numeric tables:

In[1]:=1
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https://wolfram.com/xid/0gisaa-s1u
Out[1]=1

Use Grid to format a two-dimensional table:

In[1]:=1
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https://wolfram.com/xid/0gisaa-irs
Out[1]=1

Two-dimensional numeric tables can be visualized with ArrayPlot and MatrixPlot:

In[1]:=1
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https://wolfram.com/xid/0gisaa-dqz
Out[1]=1

Print the values of the table index while the table is being generated:

In[1]:=1
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https://wolfram.com/xid/0gisaa-utg
Out[1]=1

Monitor the values by showing them in a temporary cell:

In[1]:=1
✖
https://wolfram.com/xid/0gisaa-dkpurk
Out[1]=1

Relations to Other Functions  (5)

Range gives the sequence of values of a table iterator:

In[1]:=1
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https://wolfram.com/xid/0gisaa-e5a
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0gisaa-naf
Out[2]=2

Do evaluates the same sequence of expressions as Table, but does not return them:

In[1]:=1
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https://wolfram.com/xid/0gisaa-x10
In[2]:=2
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https://wolfram.com/xid/0gisaa-ugy
Out[2]=2

Sum effectively applies Plus to results from Table:

In[1]:=1
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https://wolfram.com/xid/0gisaa-ec
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0gisaa-ic5
Out[2]=2

Array iterates over successive integers:

In[1]:=1
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https://wolfram.com/xid/0gisaa-wzj
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0gisaa-mww
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0gisaa-uvj
Out[3]=3

Map applies a function to successive elements in a list:

In[1]:=1
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https://wolfram.com/xid/0gisaa-k99str
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0gisaa-cfm7sr
Out[2]=2

Table can substitute successive elements in a list into an expression:

In[3]:=3
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https://wolfram.com/xid/0gisaa-ep4419
Out[3]=3

Nested Tables  (1)

Using multiple iteration specifications is equivalent to nesting Table functions:

In[1]:=1
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https://wolfram.com/xid/0gisaa-rxa
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0gisaa-g7s
Out[2]=2

Programmatic Table Construction  (2)

Feed in parameters for tables:

In[1]:=1
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https://wolfram.com/xid/0gisaa-ji1
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0gisaa-gdd
Out[2]=2

Use Apply to splice a complete iterator specification into Table:

In[1]:=1
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https://wolfram.com/xid/0gisaa-nti
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0gisaa-fv4
Out[2]=2

With can insert the specification for a single iterator:

In[3]:=3
✖
https://wolfram.com/xid/0gisaa-s8f
Out[3]=3

Possible Issues  (6)Common pitfalls and unexpected behavior

For some step sizes, output from Table may not include the upper limit given:

In[1]:=1
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https://wolfram.com/xid/0gisaa-efvbkl
Out[1]=1

Table requires list iterator specifications to be given explicitly:

In[1]:=1
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https://wolfram.com/xid/0gisaa-n1x
Out[1]=1

Forcing early evaluation of the list resolves the issue:

In[2]:=2
✖
https://wolfram.com/xid/0gisaa-n96
Out[2]=2

Alternatively, using With to lexically replace p with its list form:

In[3]:=3
✖
https://wolfram.com/xid/0gisaa-j9n
Out[3]=3

Table normally reevaluates at each step:

In[1]:=1
✖
https://wolfram.com/xid/0gisaa-hnl
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0gisaa-q4b
Out[2]=2

The Evaluate is needed to force evaluation of the table before it is fed to Plot:

In[1]:=1
✖
https://wolfram.com/xid/0gisaa-vi0
Out[1]=1

Compare with:

In[2]:=2
✖
https://wolfram.com/xid/0gisaa-synfm
Out[2]=2

Values of Table variables do not get substituted inside held expressions:

In[1]:=1
✖
https://wolfram.com/xid/0gisaa-y9z
Out[1]=1

Use With to insert values:

In[2]:=2
✖
https://wolfram.com/xid/0gisaa-whw
Out[2]=2

Formatting wrappers such as Grid give expressions that are no longer lists:

In[1]:=1
✖
https://wolfram.com/xid/0gisaa-wbv
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0gisaa-ve7
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0gisaa-ltw
Wolfram Research (1988), Table, Wolfram Language function, https://reference.wolfram.com/language/ref/Table.html (updated 2015).
✖
Wolfram Research (1988), Table, Wolfram Language function, https://reference.wolfram.com/language/ref/Table.html (updated 2015).

Text

Wolfram Research (1988), Table, Wolfram Language function, https://reference.wolfram.com/language/ref/Table.html (updated 2015).

✖
Wolfram Research (1988), Table, Wolfram Language function, https://reference.wolfram.com/language/ref/Table.html (updated 2015).

CMS

Wolfram Language. 1988. "Table." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/Table.html.

✖
Wolfram Language. 1988. "Table." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/Table.html.

APA

Wolfram Language. (1988). Table. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Table.html

✖
Wolfram Language. (1988). Table. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Table.html

BibTeX

@misc{reference.wolfram_2025_table, author="Wolfram Research", title="{Table}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/Table.html}", note=[Accessed: 30-March-2025 ]}

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@misc{reference.wolfram_2025_table, author="Wolfram Research", title="{Table}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/Table.html}", note=[Accessed: 30-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_table, organization={Wolfram Research}, title={Table}, year={2015}, url={https://reference.wolfram.com/language/ref/Table.html}, note=[Accessed: 30-March-2025 ]}

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@online{reference.wolfram_2025_table, organization={Wolfram Research}, title={Table}, year={2015}, url={https://reference.wolfram.com/language/ref/Table.html}, note=[Accessed: 30-March-2025 ]}